Find the surface area of the square pyramid. 15 ft 16 ft 16 ft

To find the surface area of a square pyramid, we need to calculate the area of its base and the area of its four triangular faces.<br /><br />Given:<br />- The side length of the base (a) = 16 ft<br />- The slant height (l) = 15 ft<br /><br />1. **Calculate the area of the base:**<br /><br />The base is a square, so its area is given by:<br /><br />\[ \text{Area of base} = a^2 = 16 \times 16 = 256 \, \text{ft}^2 \]<br /><br />2. **Calculate the area of the four triangular faces:**<br /><br />Each triangular face has a base equal to the side of the square and a height equal to the slant height of the pyramid. The area of one triangular face is:<br /><br />\[ \text{Area of one triangle} = \frac{1}{2} \times \text{base} \times \text{slant height} = \frac{1}{2} \times 16 \times 15 = 120 \, \text{ft}^2 \]<br /><br />Since there are four triangular faces, the total area of the triangular faces is:<br /><br />\[ \text{Total area of triangles} = 4 \times 120 = 480 \, \text{ft}^2 \]<br /><br />3. **Calculate the total surface area of the pyramid:**<br /><br />The total surface area is the sum of the area of the base and the area of the four triangular faces:<br /><br />\[ \text{Total surface area} = \text{Area of base} + \text{Total area of triangles} = 256 + 480 = 736 \, \text{ft}^2 \]<br /><br />Therefore, the surface area of the square pyramid is \( 736 \, \text{ft}^2 \).